On the structure of split regular -Hom-Jordan-Lie superalgebras
Resumo
In this paper we study the structure of arbitrary split regular -Hom-Jordan-Lie super algebras. By developing techniques of connections of roots for this kind of algebras, we show that such a split regular -Hom-Jordan-Lie superalgebra L is of the form
L = H
[
]
Σ
[
]2= V
[
]; with H
[
] a graded linear subspace of the graded abelian subalgebra H and any V [ ]; a well-described ideal of L; satisfying [V [ ]; V []] = 0 if [
] ̸= []: Under certain conditions, in the case of L being of maximal length, the simplicity of the algebra is characterized and it is shown that L is the direct sum of the family of its minimal ideals, each one being a simple split regular -Hom-Jordan-Lie superalgebra.
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